Answer:
[tex]\begin{gathered} PY\text{ = 30 }cm \\ XQ\text{ = 2.5 }cm \end{gathered}[/tex]
Explanation:
Here, we want to determine the length of PY and XQ
From what we have here, there are 2 triangles, a smaller one sitting on top a larger one
When two triangles are similar, the ratio of their corresponding sides are equal
Mathematically, we have it that:
[tex]XY\text{ = XP + PY }[/tex]
We have it that XY = 35 cm and PX is 5 cm
Thus:
[tex]\begin{gathered} PY\text{ = XY-XP} \\ PY\text{ = 35-5 = 30 }cm \end{gathered}[/tex]
Secondly, we want to get the length of XQ as follows:
[tex]\begin{gathered} \frac{XP}{XY}\text{ }=\text{ }\frac{XQ}{XZ} \\ \\ XZ\text{ = XQ+ 15} \\ \text{Let us call XQ x} \\ We\text{ have it that:} \\ \frac{5}{35}\text{ = }\frac{x}{x+15} \\ 5(x+15)\text{ = 35(x)} \\ 5x+75\text{ = 35x} \\ 75\text{ = 35x-5x} \\ 30x\text{ = 75} \\ x=\text{ }\frac{75}{30} \\ x=\text{ }\frac{5}{2} \\ x\text{ = 2.5 }cm\text{ } \\ XQ\text{ = 2.5 }cm \end{gathered}[/tex]
